Is there a technical name for image classification on amount instead of class?
Training a system to predict real numbers instead of classes is called regression. If you had a training data where the inputs were images of water glasses and the targets were the amount of water in each glass, then this would be regression task from images of water glasses to the amount of water in each glass. You could call it image regression in the same way you would say image classification, but beyond that, I don't think there's a special term for regression where the inputs are images.